Elliptic curve cryptography with fragmented key processing and methods for use therewith

Abstract

A cryptography module includes a key store having a plurality of storage locations for storing a private key as k key fragments. One or more crypto-processing segments each operate based on corresponding ones of the k key fragments to process a message in accordance with elliptic curve digital signature algorithm (ECDSA) to produce a signed message.

What is claimed is: 
     
       1. A cryptography module comprising:
 a key store having a plurality of storage locations for storing a private key as k key fragments that include k−1 key segments and a remainder key fragment, where k is greater than 2, wherein the k−1 key segments are generated as random key segments, and wherein the remainder key fragment is generated based on the k−1 key segments; and 
 at least one crypto-processing segment, coupled to the key store, operating based on the k key fragments for processing a message in accordance with elliptic curve digital signature algorithm (ECDSA) to produce a signed message. 
 
     
     
       2. The cryptography module of  claim 1  wherein the at least one crypto-processing segment generates a modular product based on corresponding ones of the k key fragments. 
     
     
       3. The cryptography module of  claim 1  wherein the at least one crypto-processing segment sequentially processes the message based on the k key fragments to produce the signed message. 
     
     
       4. The cryptography module of  claim 1  wherein the at least one crypto-processing segments includes a plurality of crypto-processing segments that operate in parallel to process the message into a plurality of fragmented key results and wherein the cryptography module further comprises:
 a combiner, coupled to the plurality of crypto-processing segments, that combines the plurality of fragmented key results to produce the signed message. 
 
     
     
       5. The cryptography module of  claim 4  wherein the combiner generates a sum of the plurality of fragmented key results. 
     
     
       6. The cryptography module of  claim 1  wherein:
     d =( m   1   +m   2   +m   3   + . . . +m   k )modulo  n    
 where m i  represents the ith of the k key fragments, d represents the key and n is an integer. 
 
     
     
       7. A method comprising:
 storing a private key in k key fragments that include k−1 key segments and a remainder key fragment, where k is greater than 2, wherein the k−1 key segments are generated as random key segments, and wherein the remainder key fragment is generated based on the k−1 key segments; and 
 processing a message in accordance with elliptic curve digital signature algorithm (ECDSA) via at least one crypto-processing segment, based on the k key fragments, to produce a signed message. 
 
     
     
       8. The method of  claim 7  wherein the at least one crypto-processing segment generates a modular product based on corresponding ones of the k key fragments. 
     
     
       9. The method of  claim 7  wherein processing the message includes sequentially processing the message to produce the signed message. 
     
     
       10. The method of  claim 7  wherein processing the message includes:
 processing the message in parallel to generate a plurality of fragmented key results; and 
 combining the plurality of fragmented key results to produce the signed message. 
 
     
     
       11. The method of  claim 7  wherein combining the plurality of fragmented key results includes generating a sum of the plurality of fragmented key results. 
     
     
       12. The method of  claim 7  wherein:
     d =( m   1   +m   2   +m   3   + . . . +m   k )modulo  n    
 where m i  represents the ith of the k key fragments, d represents the key and n is an integer. 
 
     
     
       13. A method comprising:
 generating at least one random number via a random number generator; 
 generating k−1 key fragments via a device based on the at least one random number, where k is greater than 2; and 
 generating a remainder key fragment via the device, based on a modulo remainder computed from the k−1 key fragments and a key; 
 wherein the key includes a private key of a elliptic curve digital signature algorithm (ECDSA).